When the parameters of a quantum system are slowly cycled around a closed path, a geometric phase is acquired in addition to the dynamical phase for the quantum state [1]}. In the past 30 years, the geometric phase has been shown to have broad applications in many areas of physics, including quantum technology [2]}, [3]}, [4]}, [5]}, cold atom physics [6]}, [7]}, condensed-matter physics [8]}, and optics [9]}. In optics, the geometric phase commonly refers to the Pancharatnam-Berry (PB) phase, which usually applies to light propagating through an optical medium with slowly changing polarization or direction of photons. It is widely used for beam shaping [10]}, [11]}, shearing [12]}, guiding [13]}, trapping [14]}, holography [15]}, and encoding of classical [16]} or quantum [17]} information. Very recently, a photonic spin-Hall effect was created by a wavevector-varying PB phase [18]}.
